David W. Eggert

An experimental comparison of range image segmentation algorithms

A methodology for evaluating range image segmentation algorithms is proposed. This methodology involves (1) a common set of 40 laser range finder images and 40 structured light scanner images that have manually specified ground truth and (2) a set of defined performance metrics for instances of correctly segmented, missed, and noise regions, over- and under-segmentation, and accuracy of the recovered geometry. A tool is used to objectively compare a machine generated segmentation against the specified ground truth. Four research groups have contributed to evaluate their own algorithm for segmenting a range image into planar patches.

Estimating 3-D rigid body transformations: a comparison of four major algorithms

Abstract.A common need in machine vision is to compute the 3-D rigid body transformation that aligns two sets of points for which correspondence is known. A comparative analysis is presented here of four popular and efficient algorithms, each of which computes the translational and rotational components of the transform in closed form, as the solution to a least squares formulation of the problem. They differ in terms of the transformation representation used and the mathematical derivation of the solution, using respectively singular value decomposition or eigensystem computation based on the standard

Simultaneous Registration of Multiple Range Views for Use in Reverse Engineering of CAD Models

[ \vec{R}, \vec{T} ]

A comparison of four algorithms for estimating 3-D rigid transformations

representation, and the eigensystem analysis of matrices derived from unit and dual quaternion forms of the transform. This comparison presents both qualitative and quantitative results of several experiments designed to determine (1) the accuracy and robustness of each algorithm in the presence of different levels of noise, (2) the stability with respect to degenerate data sets, and (3) relative computation time of each approach under different conditions. The results indicate that under “ideal” data conditions (no noise) certain distinctions in accuracy and stability can be seen. But for “typical, real-world” noise levels, there is no difference in the robustness of the final solutions (contrary to certain previously published results). Efficiency, in terms of execution time, is found to be highly dependent on the computer system setup.

High-level cad model acquisition from range images

When reverse engineering a CAD model, it is necessary to integrate information from several views of an object into a common reference frame. Given a rough initial alignment of local 3-D shape data in several images, further refinement is achieved using an improved version of the recently popular Iterative Closest Point algorithm. Improved data correspondence is determined by considering the merging data sets as a whole. A potentially incorrect distance threshold for removing outlier correspondences is not needed as in previous efforts. Incremental pose adjustments are computed simultaneously for all data sets, resulting in a more globally optimal set of transformations. Individual motion updates are computed using force-based optimization, by considering the data sets as implicitly connected by groups of springs. Experiments on both 2-D and 3-D data sets show that convergence is possible even for very rough initial positionings, and that the final registration accuracy typically approaches less than one quarter of the interpoint sampling resolution of the images.

Simultaneous registration of multiple range views for use in reverse engineering

A common need in machine vision is to compute the 3-D rigid transformation that exists between two sets of points for which corresponding pairs have been determined. In this paper a comparative analysis of four popular and efficient algorithms is given. Each computes the translational and rotational components of the transform in closed-form as the solution to a least squares formulation of the problem. They differ in terms of the representation of the transform and the method of solution, using respectively: singular value decomposition of a matrix, orthonormal matrices, unit quaternions and dual quaternions. This comparison presents results of several experiments designed to determine the (1) accuracy in the presence of noise, (2) stability with respect to degenerate data sets, and (3) relative computation time of each approach.

Computing the perspective projection aspect graph of solids of revolution

Abstract Automatic extraction of cad descriptions which are ultimately intended for human manipulation requires the accurate inference of geometric and topological information. We present a system which applies segmentation techniques from computer vision to automatically extract cad models from range images of parts with curved surfaces. The segmentation process is an improvement upon Besl and Jains variable-order surface fitting (IEEE PAMI, 1988, 10(2), 167–192), extracting general quadric surfaces and planes from the data, with a postprocessing stage to identify surface intersections and to extract a B-rep from the segmented image. We present results on a variety of machined objects, which illustrate the high-level nature of the acquired models, and discuss the numerical accuracy (feature sizes and separations) and the correctness of structural inferences of the system.

Computing the orthographic projection aspect graph of solids of revolution

When reverse engineering a CAD model, it is necessary to integrate information from several views of an object into a common reference frame. Given a rough initial alignment, further pose refinement here uses an improved version of the interactive closes point algorithm. Incremental adjustments are computed simultaneously for all data sets, resulting in a more globally optimal set of transformations. Also, thresholds for removing outlier correspondences are not needed, as the merging data sets are considered as a whole. Motion updates are computed through force-based optimization, using implied springs between data sets. Experiments indicate that even for very rough initial positionings, registration accuracy approaches 25% of the interpoint sampling resolution of the images.

Extracting surface patches from complete range descriptions

An algorithm for computing the aspect graph for a class of curved-surface objects based on an exact parcellation of 3-D viewpoint space is presented. The object class considered is solids of revolution. A detailed analysis of the visual events for this object class is given, as well as an algorithm for constructing the aspect graph. Numerical search techniques, based on a geometric interpretation of the visual events, have been devised to determine those visual event surfaces that cannot be calculated directly. The worst-case complexity of the number of cells in the parcellation of 3-D viewpoint space, and, hence, the number of nodes in the aspect graph, is O(N/sup 4/), where N is the degree of a polynomial that defines the object shape. A summary of the results for 20 different object descriptions is presented, along with a detailed example for a flower vase. >

Aspect Graphs And Nonlinear Optimization In 3-D Object Recognition

Abstract Several researchers have recently addressed the problem of computing the aspect graph of an object by deriving the exact partition of viewpoint space from the objects geometry. Algorithms have been developed to handle general polyhedral objects, with viewpoint space modeled as either the Gaussian sphere or as 3-D space. This paper presents the first algorithm to handle a defined class of curved-surface objects. The algorithm automatically computes the partition of the Guassian sphere, and thereby the aspect graph, for solids of revolution defined as Right, Circular, Straight, Homogeneous Generalized Cylinders.